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Mathematics > Statistics Theory

Title:Congruent families and invariant tensors

Abstract: Classical results of Chentsov and Campbell state that -- up to constant
multiples -- the only $2$-tensor field of a statistical model which is
invariant under congruent Markov morphisms is the Fisher metric and the only
invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this
result for arbitrary degree $n$, showing that any family of $n$-tensors which
is invariant under congruent Markov morphisms is algebraically generated by the
canonical tensor fields defined in an earlier paper.